I would say it plays more like John Tiller Campaign series and Squad battles than those you have listed though if you like the origonal Combat Mission games you will feel at home playing this even though there are a lot of differences most noticable being COH is impulse driven and does not model ballistics.

It is really quite unlike any of the games the OP mentions. But if I had the choice of WitE, toaw3, CMBN and CoH, CoH would be the dead-last buy. Eventually, I would still buy it though, because it's so different and challenging

There is no mistaking it as a direct board game conversion, and it includes conventions that I find quite artificial; although some would argue that the cards, bonuses and other stuff adds to the historical realism. I have had some difficulties with file management etc., on the scenario editor. Had no such trouble immediately creating scenarios for WitE, which appears more complex on the surface.

But yes, MJR, the JTCS games do come to mind as similar to CoH, along with your caveats.